Analytical solutions for ascent trajectory under high angle-of-attack conditions

To rapidly predict the ascent trajectory of launch vehicles, high-accuracy analytical solutions for ascent trajectory were proposed under high angle-of-attack (AOA) conditions. First, a simplified longitudinal-plane dynamics model with mass as the independent variable was developed. The sine of AOA was innovatively expressed as a polynomial of mass. Due to the high AOA, the simplified dynamics model remains highly nonlinear, which prevents it from being analytically solved directly. Approximate polynomials are introduced to replace the strongly nonlinear but relatively small terms in the original equations through force analysis. Furthermore, the difference between the true values and the approximations was treated as a minor perturbation. The dynamics model was divided into analytically solvable subsystems according to the perturbation theory. Analytical solutions for velocity, flight-path angle, downrange, and altitude were derived by solving the subsystems. Simulation results confirm that the proposed solutions are at least 85% more accurate than existing solutions under high AOA conditions.